Solve for $x$ and $y$ using elimination. ${-6x+3y = -33}$ ${5x-2y = 28}$
Explanation: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $3$ ${-12x+6y = -66}$ $15x-6y = 84$ Add the top and bottom equations together. $3x = 18$ $\dfrac{3x}{{3}} = \dfrac{18}{{3}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-6x+3y = -33}\thinspace$ to find $y$ ${-6}{(6)}{ + 3y = -33}$ $-36+3y = -33$ $-36{+36} + 3y = -33{+36}$ $3y = 3$ $\dfrac{3y}{{3}} = \dfrac{3}{{3}}$ ${y = 1}$ You can also plug ${x = 6}$ into $\thinspace {5x-2y = 28}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ - 2y = 28}$ ${y = 1}$